The twin-roll type strip continuous casting process(or direct rolling process) of steel materials is characterized by two rotating water cooled rolls receiving a steady supply of molten metal which solidifies onto the rolls. A solidification analysis of molten metal considering phase transformation and thermofluid is performed using finite diffefence method with curvilinear coordinate to reduce computing time and molten region analysis with arbitrary shape. An enthalpy-specific heat method is used to determine the temperatures inthe roll and the steel. The temperature distribution of cooling roll is calculated using two dimensional finite element method, because of complex roll shape due to cooling hole in rolls and improvemnt accuracy of calculation result. The energy equaiton of cooling roll is solved simultanuously with the conservation equaiton of molten metal in order to consider heat transfer through the cooling roll. The calculated roll temperature is compared to experimental results and the heat transfer coefficient between cooling roll surface and rolling material(steel) is also determined from comparison of measured roll temperature and calculated temperature.